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Foundations of Physics

, Volume 21, Issue 8, pp 983–991 | Cite as

Linear and nonlinear Schrödinger equations

  • G. Adomian
  • R. Rach
Article

Abstract

The Schrödinger equation for a point particle in a quartic potential and a nonlinear Schrödinger equation are solved by the decomposition method yielding convergent series for the solutions which converge quite rapidly in physical problems involving bounded inputs and analytic functions. Several examples are given to demonstrate use of the method.

Keywords

Analytic Function Decomposition Method Physical Problem Point Particle Convergent Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    G. Adomian, “Random eigenvalue equations,”J. Math. Anal. Appl. 3(2) (1 November 1985).Google Scholar
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    G. Adomian,Nonlinear Stochastic Operator Equations (Academic Press, New York, 1986).Google Scholar
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    G. Adomian and R. Rach, “Equality of partial solutions in the decomposition method for linear or nonlinear partial differential equations,”Comput. Math. Appl. 19(12), 9–12 (1990).Google Scholar
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    G. Adomian, “A review of the decomposition method and some recent results for nonlinear equations,”Math. Comput. Model. (1990).Google Scholar
  5. 5.
    G. Adomian,Applications of Nonlinear Stochastic Operator Equations to Physics (Reidel, Dordrecht, 1989).Google Scholar
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    Y. Cherruault, “Convergence of Adomian's method,”Kybernetes 18(2), 31–39 (1989).Google Scholar
  7. 7.
    G. Adomian, “Decomposition solution of nonlinear hyperbolic equations,”Proceedings, 7th International Conference on Mathematical Modeling, Chicago, August 1989.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • G. Adomian
    • 1
  • R. Rach
    • 1
  1. 1.Athens

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